Abstract
In this paper, we study two-component versions of the periodic Hunter–Saxton equation and its μ-variant. Considering both equations as a geodesic flow on the semidirect product of the circle diffeomorphism group with a space of scalar functions on we show that both equations are locally well posed. The main result of this paper is that the sectional curvature associated with the 2HS is constant and positive and that 2µHS allows for a large subspace of positive sectional curvature. The issues of this paper are related to some of the results for 2CH and 2DP presented in Escher et al (2011 J. Geom. Phys. 61 436–52).
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